In Problems 2 to 5 use Green’s theorem [formula ( 9.7 )] to evaluate the given
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- 3. Let be vertices (0, 0), (l,0) and (l, l). (a) Evaluate the integral 10² x³y dx - xy dy by direct calculation. Let C be the triangle with Hint: You will need to evaluate three different line integrals. A diagram will be useful! (b) Now evaluate the integral [a³y da - ry dy using Green's Theorem. (You should find this much easier!).arrow_forward.2 re² -dzdy In (x)arrow_forwardLet (z-a)" dz where a € C and the parameterization of the curve is a = {|z| = r}. Apply the fundamental theorem for integrals of complex variables and solve each part of the integral for n=1/2,1 and 2arrow_forward
- 3. Answer the following integral related questions. (1) I = Lº, (3x² – 2x + 1) dx, evaluate I;arrow_forwardAnswer 3arrow_forward9 9 9 Consider two functions f and g on [3,9] such that f(x) dx = 12, f₁(x)d = 12. Side 8 $ 148, and for 2 · g(x)dx=6, [f(x)dx=8, and [g(x)dx = 2. Evaluate the following integrals. 3 3 5 3 a. b. 5 [7f(x)dx= 28 (Simplify your answer.) 9 (f(x)- g(x))dx= (Simplify your answer.) ew an example Get more help. 3 E D C $ 4 R F > V 07 20 % 5 T G = 6 B MacBook Pro Y I' Okay H & 7 U N √₁ Vi * 00 8 J Ya 1 M ( 9 K M (0,0) O More ) O 26 Clear all 4) P V Check + [ T command optionarrow_forward
- The graph of y=f(x)…arrow_forwardWhich of the following integrals represents the length of the upper half of the ellipse + 16 1? 3 1/2 16x? dx 1 + 9(3 — х?) 16x² А. 4 1/2 В. dx 1+ 4(3 — х?) 16x? 3 1/2 1 + 9(9 — х?) 16x? C. dx 4 1/2 1 + 9(3 – x2) 16x2 D. dx 4 1/2 dx 1 + 9(9 – x²) Е. 3 1/2 16х2 dx 1 + 4(3 — х2) F. -3arrow_forwardAnswer 7arrow_forward
- Hello there! I am beginning to feel like a crazy person because I have asked the same question 6 times now and nobody has shown me the PFD for this problem. Am wondering how else I can ask to have someone help me without doing substitutions. I want to understand the PFD for the complex numbers please! Can someone please help?arrow_forward16B.2 Please help me answer all parts to this calculus problem.arrow_forwardPart I. Answer 5 onlyarrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,